Stable-by-Design Neural Network-Based LPV State-Space Models for System Identification

• URL: http://arxiv.org/abs/2510.24757v1
• Date: Tue, 21 Oct 2025 10:25:54 GMT
• Title: Stable-by-Design Neural Network-Based LPV State-Space Models for System Identification
• Authors: Ahmet Eren Sertbaş, Tufan Kumbasar,
• Abstract summary: We propose a neural network-based state-space model that simultaneously learns latent states and internal scheduling variables.<n>The state-transition matrix is guaranteed to be stable through a Schur-based parameterization.<n>The proposed NN-SS is evaluated on benchmark nonlinear systems, and the results demonstrate that the model consistently matches or surpasses classical subspace identification methods.
• Score: 6.5745172279769255
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Accurate modeling of nonlinear systems is essential for reliable control, yet conventional identification methods often struggle to capture latent dynamics while maintaining stability. We propose a \textit{stable-by-design LPV neural network-based state-space} (NN-SS) model that simultaneously learns latent states and internal scheduling variables directly from data. The state-transition matrix, generated by a neural network using the learned scheduling variables, is guaranteed to be stable through a Schur-based parameterization. The architecture combines an encoder for initial state estimation with a state-space representer network that constructs the full set of scheduling-dependent system matrices. For training the NN-SS, we develop a framework that integrates multi-step prediction losses with a state-consistency regularization term, ensuring robustness against drift and improving long-horizon prediction accuracy. The proposed NN-SS is evaluated on benchmark nonlinear systems, and the results demonstrate that the model consistently matches or surpasses classical subspace identification methods and recent gradient-based approaches. These findings highlight the potential of stability-constrained neural LPV identification as a scalable and reliable framework for modeling complex nonlinear systems.

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